Problem 53 - Basic College Mathematics

Question

Simplify. $$ \frac{238}{238} $$

Step-by-Step Solution

Answer

1

Step 1: Identify the Simplification Rule

Any non-zero number divided by itself equals 1. This is based on the property of equality in division.

Step 2: Apply the Rule

Since 238 is not zero, according to the rule identified in Step 1, \( \frac{238}{238} = 1 \).

Key Concepts

division property

When we deal with fractions, the division property is an essential concept. The division property states that any number divided by itself equals 1, provided that the number is not zero. For example, actions like dividing 5 by 5, 37 by 37, or even 1200 by 1200 can simplify to 1. This rule is crucial when simplifying fractions because it helps us reduce fractions to their simplest forms easily.

This property can be written mathematically as: \( \frac{a}{a} = 1 \) where \( a \) is any non-zero number.

equality in division

Equality in division ensures that when simplifying fractions, we maintain the balance and accuracy of the operation. For example, if we divide the numerator and the denominator of a fraction by the same non-zero number, the fraction remains equivalent. This concept applies directly to the exercise \( \frac{238}{238} \).

The rule can be seen practically in step-by-step simplifications. It helps ensure that both parts of the fraction are reduced proportionally, leading to a true and equal representation of the original fraction. Essentially, the equality in division maintains the value of the fraction during the simplification process.

fraction simplification

Fraction simplification is the process of reducing the numerator and the denominator of a fraction to their smallest, simplest form without changing the value of the fraction. In our exercise, we saw that \( \frac{238}{238} = 1 \). This means we simplified the fraction by identifying that both the numerator and denominator are the same and non-zero.

To simplify other fractions, follow these steps:

• Find common factors of the numerator and denominator.
• Divide both by their greatest common divisor (GCD).
• Repeat until the fraction is in its simplest form.

Remember, a fraction like \( \frac{50}{100} \) can simplify to \( \frac{1}{2} \) because both 50 and 100 can be divided by 50, which is their GCD.

The goal is to always achieve a simpler form that is equivalent to the original fraction.